226 On the Dispersion of the Optic Axes, &c. 



are constant. The ellipsoid itself is the reciprocal of that ellip- 

 soid by which the wave-surface is constructed, and its semiaxes 

 are the three principal indices of refraction. As X is supposed 

 to vary, not only the lengths but the directions of the principal 

 axes vary, and thus we have a different wave-surface for every 

 different wave-length within the crystal. 



The optic axes are perpendicular to the circular sections of 

 the above ellipsoid, and describe, in general, two fragments of a 

 cone, the equation of which may be found by supposing X to be 

 variable in the equation of the ellipsoid. But only very par- 

 ticular cases have been hitherto observed, and I shall not stop 

 to discuss them. 



J. MACCULLAGH. 



TRIN. COLL., PUBLIN, September, 1842. 



